Three-dimensional structured illumination microscopy (“3D-SIM”) achieves a factor of two improvement in lateral and axial resolution compared to conventional wide-field fluorescence microscopes used in cell biology. 3D-SIM requires no specialized fluorescent dyes or proteins, unlike certain competing super-resolution techniques. Biologists achieve high resolution with 3D-SIM, but retain convenient and familiar fluorescence labeling techniques. Multiple images of the subject are made with a shifting and rotating illumination pattern. Higher resolution is achieved by solving a system of equations to restore the fine spatial detail normally blurred by diffraction. A currently-available commercial 3D-SIM instrument uses a linearly polarized laser beam that is split into three or more beams by a binary phase grating. Each beam corresponds to a different diffraction order with most of the optical power concentrated in the first three diffraction orders (0th and ±1st, respectively). The 0th and ±1st order beams are focused onto the back focal plane of the microscope objective and combined to form a three-dimensional interference fringe pattern in the sample volume. 3D-SIM data are acquired by taking a fluorescence image excited by the fringe pattern, moving the grating a fifth of a period, approximately five micrometers, then taking another image, and repeating these steps for a total of five images. The grating is then rotated by 60 degrees, and the five image process is repeated, followed by another rotation and another five images, for a total of 15 images per z-step, where a z-step is a fixed point in the z-axis, coincident with the optical axis passing through the objective. Typically, at least eight z-steps are desired, for a total of 120 images per stack. These images are used to solve a system of linear equations to recover a 3D optically sectioned image with approximately double the resolution obtained by conventional wide-field microscopy. The image acquisition times involved are appreciable. Laser exposure may span 5-100 ms, camera readout may span about 50 ms per full-frame, grating motion and settlings may span tens of milliseconds, and rotation of the grating/polarization plate assembly may span roughly one full second; leading to a 3D-SIM stack acquisition time of 10-20 seconds. For the above described reasons, engineers, scientists, and microscope manufacturers continue to seek faster systems and methods for rotating the interferences pattern.